Switching from weaponsmith to armorsmith

I accidentally chose weaponsmith instead of armorsmith in blacksmithing on one of my alts. How can I change to armorsmithing? My research led me to believe that the trainer will give me the option of dropping one and picking up the other for 100 gold, but that option doesn't come up at all. I don't want to drop blacksmithing and relearn as it has probably cost me over 1000 gold to get this far. Any help would be appreciated.